Perhaps more than any other profession, science places a premium on being correct. Of course, most scientists—like most living humans—make plenty of mistakes along the way. Yet not all errors are created equal. Historians have unearthed a number of instances in which an incorrect idea proved far more potent than thousands of others that were trivially mistaken or narrowly correct. These are the productive mistakes: errors that touch on deep, fundamental features of the world around us and prompt further research that leads to major breakthroughs. Mistakes they certainly are. But science would be far worse off without them.

Niels Bohr, for example, created a model of the atom that was wrong in nearly every way, yet it inspired the quantum-mechanical revolution. In the face of enormous skepticism, Alfred Wegener argued that centrifugal forces make the continents move (or “drift”) along the surface of the earth. He had the right phenomenon, albeit the wrong mechanism. And Enrico Fermi thought that he had created nuclei heavier than uranium, rather than (as we now know) having stumbled on nuclear fission.